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Name___________________________ H. Adv. Algebra w/ Trig, period_______
SEMESTER I REVIEW
MULTIPLE CHOICE: Place the letter of the correct answer in the blank.
_______1. Evaluate the expression: 5 8 2 4 11 .
A. ‐22 B. 0
C. 15 D. ‐7
______2. Simplify: 1 112 4 35 15
4 5x x
A. 10x‐11 B. 10x‐3
C. 10x‐2 D. 21x‐3
_______3. Simplify: 2 3 5 2 1x x
A. 12 1x B. 12 11x
C. 12 2x D. 9 1x
_______4. Solve: 5 2 3 45x
A. 6 B. 6, ‐3
C. 6, 3 D.
______5. Solve: 7 18 39x
A. 21, 3 B. 28, ‐28
C. 28, ‐14 D. 28, 14
_______6. What is the solution set of 2 7 8m ?
A. 3, B. 11,
C. , 3 D. ,11
_______7. What is the solution set of 5 1 19x ?
A. 18
, 45
B. 4,4
C. , 4 D. 4,
_______8. Determine the domain of g = {(2, 7), (‐3, 8), (4, 9)} and tell if g is a function.
A. 2, 3,4 ; g is a function B. 2, 3,4 ; g is not a function
C. 7,8,9 ; g is a function D. 7,8,9 ; g is not a function
_______9. Determine the domain of h = {(5, 10), (6, 20), (5, 30)} and tell if h is a function.
A. 5,6 ; h is a function B. 5,6 ; h is not a function
C. 10,20,30 ; h is a function D. 10,20,30 ; h is not a function
_______10. Determine the domain of k = {(‐4, 14), (‐5, 14), (‐6, 16), (‐7, 16)} and tell if k is a function.
A. 4, 5, 6, 7 ; k is a function B. 4, 5, 6, 7 ; k is not a function
C. 14,16 ; k is a function D. 14,16 ; k is not a function
_______11. Determine the domain of the given graph.
A. , B. 1,7
C. ,5 D. ,3
_______12. Determine the range of the given graph.
A. , B. ,5
C. 5, D. 1,7
______13. Find g(‐2) if 2
( )1
xg x
x
.
A. 2
5
B.
2
3
C. 2 D.
1
5
______14. Find h(3) if 2 2 1
( )1
x xh x
x
.
A. 7
2 B.
7
3 C. 2 D. ‐2
(3, 5)
(7, 0) (‐1, 0)
. ..
(3, 5)
(7, 0) (‐1, 0)
. ..
______15. For which equation is the graph a horizontal line? A. y = x ‐1 B. 8 + y = 4 C. x = 7 D. y = x ______16. For which equation is the graph a vertical line?
A. y = x B. 3+ y = 5 C. x + 1 = 9 D. y = x
______17. What is the slope of a horizontal line? A. 1 B. ‐1 C. 0 D.
______18. What is the slope of a vertical line? A. 1 B. ‐1 C. 0 D.
______19. For which pair of equations are the lines parallel?
A. 2x + 5y = 12 B. x + 3y = 15 C. y = 2x + 5 D. y = 1
4
x
5x + 2y = 12 x = ‐3y + 6 y = 5x + 2 y = 4x ______20. What is the slope of a line that is perpendicular to the graph of 4x – y = 8?
A. 4 B. ‐4 C. 1
4 D.
1
4
_______21. What is the standard form of an equation for a line that passes through (1, ‐5) and has a slope of ‐4?
A. 4 1x y
B. 4 1x y
C. 4 9x y
D. 4 9x y
_______22. What is the standard form of an equation for a line that passes through (2, 7) and has a slope of 1
2?
A. 2 3x y
B. 2 11x y
C. 2 12x y
D. 2 16x y
_______23. Data is collected showing the number of pretzels(y) bought at a local mall every hour (x) for the first six hours after opening. Assuming that a linear relation exists, identify the regression function that best describes the data.
A. 1.17 16.4y x B. 1.03 18.9y x
C. 1.17 18.9y x D. 1.03 16.4y x
Hour after opening, x 1 2 3 4 5 6
# of pretzels, y 17 20 19 22 21 24
_______24. Super Sally, a truly amazing individual, picks up a rock and throws it as hard as she can. The table below displays the relationship between the rock’s horizontal distance (y) in feet from Sally and the initial speed (x) with which she throws. Assuming that a linear relation exists, identify the regression function that best describes the data.
A. 0.926 0.79y x B. 1.077 0.79y x
C. 0.926 0.78y x D. 1.077 0.78y x
______25. What is the vertex for the graph of ( ) 4 3f x x ?
A. (4, 3) B. (4, ‐3) C. (‐3, 0) D. (3, 0)
_______26. Which is the graph of 2y x ?
A. B.
C. D.
_______27. Which is the graph of 4y x ?
A. B.
C. D.
Initial Speed (ft/sec), x 10 15 20 25 30
Horizontal Distance (ft), y 9.9 14.8 19.1 24.5 28.2
(0, 0)
(‐2, ‐2)
(2,0)
(0, ‐2)
(‐2, 0)
(2,0)
(3, 3) (1, 3)
(‐1,1) (‐3, 1)
(‐2, 0) . . . . ..
.. . .
.
(4, 0)
(0, ‐4)
. .
.(‐4, 0)
(4, 0)
(5, 1) . . . (3, 1) (‐1,3) (‐3, 3) .. .
(‐4, 0)
(2, 6)
(0, 4)
. .
. (‐2, 6)
_______28. Which is the graph of x – 3y = 9? A. B.
C. D.
_______29. Which is the graph of 2 3x ? A. B.
C. D.
______30. Solve the system of equations. What is the x value?
2 8
2 2 3
3 4 1
x y z
x y z
x y z
A. 4 B. ‐1 C. 5 D. 2
(‐9, 0)
(0, ‐3)
. . (9, 0) (0, ‐3) . .
(‐9, 0)
(0, 3)
. .
(0, ‐9)
(3, 0) ..
(‐2, 0)
(0, 3)
..
(5, 0) .
(2, 0)
(0, ‐3)
..
(0, 5) .
______31. Solve the system of equations. What is the x value? A. ‐5 B. ‐4 C. 5 D. 4 ____32. For which system of equations is there no solution?
A. 4 15
2 4 8
x y
x y
B. 3 8 11
9 24 33
x y
x y
C. 5 6
5 12
x y
x y
D. 3 1
3 2
y x
y x
____33. For which system of equations are there infinitely many solutions?
A. 4 15
2 4 8
x y
x y
B. 3 8 11
9 24 33
x y
x y
C. 5 6
5 12
x y
x y
D. 3 1
3 2
y x
y x
______34. Which of the following satisfies the system of inequalities?
3
8
1
y x
y
x
A. (4, 0) B. (4, ‐4) C. (0, 4) D. (4, 4)
_____35. Graph the function 5 2y x
A. B. C. D. _____36. Graph the function A. B. C. D.
_____37. Graph the function A. B. C. D.
______38. Which of the following functions represents the graph of 3y x with a translation
of 10 units to the right?
A) 3 10y x B) 3 10y x
C) 3 10y x D) 3
10y x
______39. How is the graph of 7y x translated from the graph of y x ?
A) shifted 7 units right B) shifted 7 units left C) shifted 7 units up D) shifted 7 units down
______40. Identify the domain of the function ( ) 3 1f x x
A) 3, B) 1,
C) 3, D) ,
______41. Identify the domain of the function ( ) 5 3f x x
A) 5, B) ,
C) 5, D) 3,
______42. Beth is a dietician for a hospital and must order x units of vegetables and y units of meat for the coming week. The minimum daily requirements recommends at least 10 units of protein and 14 units of vitamins. Use the provided table to determine which system of inequalities Beth should use to decide how many units of vegetables and meat to order to obtain the minimum daily requirements?
A.
3 7 10
5 2 14
0
0
x y
x y
x
y
B.
3 7 10
5 2 14
0
0
x y
x y
x
y
C.
3 5 10
7 2 14
0
0
x y
x y
x
y
D.
3 5 10
7 2 14
0
0
x y
x y
x
y
protein vitamins
1 unit of veggies =x 3 5
1 unit of meat=y 7 2
_____43. Beth is a dietician for a hospital and must order vegetables and meats for a patient. A patient has a special diet that requires at least 8 units of protein and at least 12 units of vitamins. Use the table provided to determine which system of inequalities Beth should use to order vegetables and meats for this patient?
A.
3 7 8
5 2 12
0
0
x y
x y
x
y
B.
3 7 12
5 2 8
0
0
x y
x y
x
y
C.
3 5 8
7 2 12
0
0
x y
x y
x
y
D.
3 5 12
7 2 8
0
0
x y
x y
x
y
______44. Jim invested a total of $25000 in three different stocks: Acme paying 4.5% per year, Beeps paying 6% per year, and Wile‐E paying 8.2% per year. Conservative in his strategy, Jim invested twice as much money in lower risk Acme as he did in higher risk Wile‐E. If Jim earned $1442 in one year, how much money did he invest in Beeps? A. $12,300
B. $6300 C. $3250 D. $2150
DETERMINE WHETHER EACH STATEMENT IS TRUE OR FALSE.
____________45. 4 6 105 5 5
____________46. 2 2 2a b a b
____________47. 3 3 32x x x
____________48. 32 7 5 10m n m n
MULTIPLE CHOICE: Place the letter of the correct answer in the blank.
______49. Simplify: 3 5 4 24 2 5x y xy xy A. 3 20 3 106 9x y x y
B. 4 9 4 76 9x y x y
C. 3 20 3 108 20x y x y
D. 4 9 4 78 20x y x y
protein vitamins
1 unit of veggies =x 3 7
1 unit of meat=y 5 2
______50. Simplify: 24 37x y
A) 6
849
y
x B)
6
8
14y
x
C) 2
5
5x
y D)
6 5
14
x y
______51. Simplify: 22
3
4
2
xy
xy
A. 332
y
x B.
32
y
C. 3 7
4
x y D. 3
8y
x
______52. Simplify: 32 4
7 3
3
6
a bc
a bc
A. 9
5 43
c
a b B.
9
5 42
c
a b
C. 9
5 22
c
a b D.
5 4 15
1
3a b c
______53. 2
1?
5
A) 1
10 B) 25
C) 1
25 D) 10
______54. Simplify: 3 2 34 7 8 2 6 1x x x x
A.
3 26 7 6 7x x x B. 6 28 7 6 9x x x
C. 9 22 7 6 9x x x D. 3 22 7 6 7x x x
______55. Simplify: 2 25 9 4 2 5 3x x x x
A. 27 4 1x x B. 4 23 14 7x x
C. 23 14 7x x D. 23 4 1x x
______56. Multiply: 23x y
A. 2 29x y B. 2 29x y
C. 2 26 9x xy y D. 2 26 9x xy y
______57. Factor completely: 22 8x A. 2( 2)( 2)x x B. (2 1)( 8)x x
C. 22( 2)x D. (2 2)( 4)x x
______58. Factor completely: 3 264 48 4 3x x x
A. 2(64 48 4 ) 3x x x x B. 4 1 4 1 4 3x x x
C. 24 1 4 3x x D. 216 4 3 4 3x x x
______59. Factor completely: 32 250y
A. 22 25 10y y B. 22 5 5 25y y y
C. 22 5 50y y D. 22 5 5 25y y y
______60. Factor completely: 3 29 6 12 8x x x
A. 23 2 3 4x x B. 23 2 3 4x x
C. 23 2 3 2x x D. 23 4 3 2x x
______61. 2 26 8 = ?
A) 14 B) 14 C) 10 D) 196
______62. Simplify: 7 163 50x x y
A) 4 415 2x y x B) 4 875 2x y x
C) 4 815 2x y x D) 3 415 2x y x
______63. Simplify: 8 143 128x y
A) 2 4 2 234 2x y x y B) 2 4 2 24 2x y x y
C) 2 4 2 22 16x y x y D) 2 4 2 232 16x y x y ______64. Simplify the radical expression:
5 4 7 92 32x y x y
A) 6 616 4x y y B) 6 68x y y
C) 5 6 24 4x y x y D) 17 184 4x y x
______65. Express 16 12 363 9x y z using exponents.
A) 8 1
4 23 23 x y z B) 1 8 1
23 3 29 x y z
C) 8 1
3 23 29 x y z D) 4 8 1
23 3 23 x y z
______66. Express 3
5x in radical form.
A) 5 3x B) 3 5x
C) 3
5x D) 5
3
x
______67. Express as a single radical in simplest form: 24 36x
A) 6 x B) 6x
C) 6x D) 4 6x
______68. Express as a single radical in simplest form: 6 44x
A) 3 22x B) 2 6 4x
C) 3 22 x D) 3 24x
______69. 64 36 64 36
A) true B) false
______70. Simplify 3 27
A) 9i B) 9i C) 9 D) 9
______71. Simplify 2 10
A) 20 B) 2 5
C) 2 5 D) 2 5i
_____72. Multiply: 6 2 3
A) 6 2 3 B) 12 18
C) 5 5 D) 2 3 3 2
______73. Simplify: 33
2
A)
32 3
2 B)
3 12
2
C)
3 3
2 D)
3 6
2
______74. Simplify:
A)
3 48
4 B)
3 12
4
C) 3 3
2 D)
3 6
2
______75. Simplify:
2 23 15
A) 5
x y
x
2 23 3B)
x y
x
C)
23 75
25
xy
x D) 23 3xy
______76. Simplify. 3
1 5
A) 1 3 5
2
B)
3 3 5
4
C) 3 3 5
24
D) 3 3 5
4
______77. Simplify: 7 2
7 2
A) 51 14 2
47
B)
51 14 2
47
C) 1 D) 47 14 2
51
______78. Solve: 7 2x x
A) x =9
16 B) x =
4
25
C) x =5
4 D)
2
33
25
y
x
33
4
______79. Solve: 6 2x x
A) 2x B) 4x C) 1x D)
______80. Solve: 12 2x x
A) 2x B) 4x C) 16x D)
______81. Solve: 9 1 2x x
A) 16x B) 27x C) 30x D)
_____82. Solve: 26 25x x A) 3 4i B) 3 8i C) 3 4i D) 3 8i
_____83. Solve: 26 13 5 0n n
A) 1 5
, 2 3
B) 1 5
, 3 2
C) 1 5
, 2 3
D) 1 5
, 3 2
______84. Solve: 24 9y y
A) 4
9 B) 0
C) 4
,09
D) 4
,09
______85. When solving an equation by completing the square, what number should be added to both sides of the following equation?
2 10 ____ 7 ____x x A) 25 B) 5
C) 100 D) 25
4
______86. Use the discriminant to describe the number and type of roots of the equation:
25 4 6 0x x . A) 2 complex roots B) 1 real root C) 1 complex root D) 2 real roots
______87. Reduce:4 8 6
12
i
A) 1 8 6
3
i B)
1 2 6
3
i
C) 2 4 6
6
i D) 2 2 2i
______88. The graph of a quadratic function is shown at the right. What are the solutions of the related quadratic equation? A) x = 4, ‐2 B) x = ‐1, ‐9 C) x = ‐4, 2 D) x = 0, ‐8
______89. What is the vertex of the parabola defined by 22 3y x ?
A) (‐2, 3) B) (‐3, 0) C) (0, 3) D) (0, ‐3) ______90. What is the equation of the parabola shown at the right?
A) 22 6y x
B) 22 6y x
C) 22 6y x
D) 22 6y x
______91. What is the equation of the axis of symmetry of the parabola defined by 22 5 1y x ?
A) x = 1 B) x = ‐5 C) x = 5 D) x = 2 ______92. Which inequality is graphed at the right?
A) 216
2y x
B) 216
2y x
C) 216
2y x
D) 216
2y x
______93. Solve the inequality: 22 7 9x x
9 9A) / 1 or , 1 ,
2 2x x or x
9 9B) / 1 and or 1, ,
2 2x x x
9 9C) / 1 or , 1, C)
2 2x x or x
9 9
D) / 1 or 1,2 2
x x
______94. Solve the inequality: 3 23 28 0x x x
A) | 4 0 7 or , 4 0,7x x or x
B) | 7 0 4 or 7,0 4,x x or x
C) | 4 0 7 or 4,0 7,x x or x
D) | 4 or 4,x x
______95. Solve the inequality: 22 9 5 0x x
A) 1 1| 5 or , 5,
2 2x x or x
B) 1 1
| 5 or ,52 2
x x
C) 1 1| 5 or , 5 ,
2 2x x or x
D) 1 1
| 5 or 5,2 2
x x
______96. A golfball is hit upward with a velocity of 60 feet per second. Its height above the ground after t seconds is
given by 2( ) 16 60h t t t . What is the maximum height in feet reached by the ball?
A) 1.88 feet B) 56.25 feet C) 62,75 feet D) 74.78 feet ______97. A golfball is hit upward with a velocity of 40 feet per second. Its height above the ground after t seconds is
given by 2( ) 16 40h t t t . What is the maximum height in feet reached by the ball?
A) 25 feet B) 125 feet C) 30 feet D) 130 feet
Solve each of the following problems. Show all work. Place your answer in the blank provided.
98. Solve: 2 1
12 3 6 4
x x 98._____________________________
99. What is the slope‐intercept form of the equation of a line that passes through (1, 6) and is parallel to a line whose equation is 6x – 2y = 8? 99. ____________________________ 100. What is the slope‐intercept form of the equation of a line that passes through (1, 6) and is perpendicular to a line whose equation is 2x – 5y = ‐20? 100. ____________________________
101. Tim invested a total of $13,000 in three different investments: stocks paying 6% per year, bonds paying 4% per year, and certificates of deposit paying 3% per year. Tim invested twice as much money in bonds as stocks. If Tim earned $540 in one year, how much money did he invest in certificates of deposit?
Define the vbl. equation or inequality/solve solution
101. ____________________________
102. Jim invested a total of $15,000 in three different investments: stocks paying 7% per year, bonds paying 5% per year, and certificates of deposit paying 2% per year. Jim invested twice as much money in bonds as stocks. If Jim earned $795 in one year, how much money did he invest in stocks?
Define the vbl. equation or inequality/solve solution
102. ___________________________
Divide each of the following.
103. 3 26 17 18 23 3 4x x x x 104. 3 25 7 7 8 5 2x x x x
103. _____________________________ 104. _____________________________
Graph each system of inequalities.
105. 2 4
13
3
y x
y x
106.
15
23 2
y x
y x
107.
2 3
31
5
y x
y x
Graph each function. Name the domain and range.
108. 109.
2 3 if 1
( ) 6 if 1 4
5 if 4
x x
f x x
x x
D=________________ D=________________ R=________________ R=________________
2 if 0 ( )
if 0
xf x
x x
Factor each of the following expressions completely.
110. 210 7 12y y 111. 3125 8x 112. 327 64y
110. ________________________ 111. ________________________ 112. ________________________
Solve each equation.
113. 25 3 2 0x x 114. 2 6 0x x 113. _____________________________ 114. _____________________________
Express each of the following in vertex form.
115. 2( ) 3 12 1f x x x 116. 2( ) 4 8 3f x x x 117. 2( ) 2 4 5f x x x
115. ________________________ 116. ________________________ 117. ________________________
1. B
2. C 3. A 4. B 5. C 6. A 7. C 8. A 9 . B 10. A 11. A 12. B 13. A 14. C 15. B 16. C 17. C 18. D 19. B 20. D 21. A 22. C 23. A 24. C 25. D 26. C 27. B 28. B 29. A 30. A 31. C 32. D 33. B 34. C 35. B 36. A 37. C 38. D 39. C 40. A 41. B 42. A 43. C 44. C 45. true 46. false 47. true 48. false
49. D 50. A 51. A 52. B 53. B 54. D 55. C 56. C 57. A 58. B 59. D 60. A 61. C 62. C 63. A 64. B 65. D 66. A 67. C 68. A 69. B 70. C 71. C 72. D 73. B 74. D 75. A 76. D 77. A 78. A 79. A 80. D 81. B 82. C 83. D 84. D 85. A 86. D 87. B 88. C 89. C 90. D 91. B 92. A 93. A
94. C 95. D 96. B 97. A 98. x = 11 99. y = 3x + 3
100. 5 17
2 2y x
101. $4000 102. $4500
103. 2 152 3 2
3 4x x
x
104. 2 61
5 2x x
x
110. 2 3 5 4y y
111. 25 2 25 10 4x x x
112. 23 4 9 12 16y y y
113. 3 31
10
i
114. 1 23
2
i
115. 2( ) 3 2 11f x x
116. 2( ) 4 1 1f x x
117. 2( ) 2 1 3f x x
SEMESTER I REVIEWANSWERS
105.
106.
107.
108. 109.
D= , R= 2, 2 0, D= , R= ,1 6,6
